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3 years ago

Problem page the length of a rectangle is six times its width. if the perimeter of the rectangle is 98 cm , find its area.

1 answer:

4 0

Let width be x.

Length: 6x

P=2(l+w)
98=2(6x+x)
98/2=7x
49=7x
49/7=x
7=x

Therefore, the width is 7 and the length is 7*6=42

Area=lw
A=(42)(7)
A=294 cm²

Hope I helped :)

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You work at a pioneer historical site. On this site you have handcarts. One cart has a handle that connects to the center of the

Gelneren [198K]

Answer:

a) see below

b) radius = 16.4 in (1 d.p.)

c) 18°. Yes contents will remain. No, handle will not rest on the ground.

d) Yes contents would spill. Max height of handle = 32.8 in (1 d.p.)

Step-by-step explanation:

Part a

A chord is a line segment with endpoints on the circumference of the circle.

The diameter is a chord that passes through the center of a circle.

Therefore, the spokes passing through the center of the wheel are congruent chords.

The spokes on the wheel represent the radii of the circle. Spokes on a wheel are usually evenly spaced, therefore the congruent central angles are the angles formed when two spokes meet at the center of the wheel.

Part b

The tangent of a circle is always perpendicular to the radius.

The tangent to the wheel touches the wheel at point B on the diagram. The radius is at a right angle to this tangent. Therefore, we can model this as a right triangle and use the tan trigonometric ratio to calculate the radius of the wheel (see attached diagram 1).

$\sf \tan(\theta)=\dfrac{O}{A}$

where:

$\theta$ is the angle
O is the side opposite the angle
A is the side adjacent the angle

Given:

$\theta$ = 20°
O = radius (r)
A = 45 in

Substituting the given values into the tan trig ratio:

$\implies \sf \tan(20^{\circ})=\dfrac{r}{45}$

$\implies \sf r=45\tan(20^{\circ})$

$\implies \sf r=16.37866054...$

Therefore, the radius is 16.4 in (1 d.p.).

Part c

The measure of an angle formed by a secant and a tangent from a point outside the circle is half the difference of the measures of the intercepted arcs.

If the measure of the arc AB was changed to 72°, then the other intercepted arc would be 180° - 72° = 108° (since AC is the diameter).

$\implies \sf new\: angle=\dfrac{108^{\circ}-72^{\circ}}{2}=18^{\circ}$

As the handle of the cart needs to be no more than 20° with the ground for the contents not to spill out, the contents will remain in the handcart at an angle of 18°.

The handle will not rest of the ground (see attached diagram 2).

Part d

This can be modeled as a right triangle (see diagram 3), with:

height = (48 - r) in
hypotenuse ≈ 48 in

Use the sin trig ratio to find the angle the handle makes with the horizontal:

$\implies \sf \sin (\theta)=\dfrac{O}{H}$

$\implies \sf \sin (\theta)=\dfrac{48-r}{48}$

$\implies \sf \sin (\theta)=\dfrac{48-45\tan(20^{\circ})}{48}$

$\implies \theta = 41.2^{\circ}\:\sf(1\:d.p.)$

As 41.2° > 20° the contents will spill out the back.

To find the maximum height of the handle from the ground before the contents start spilling out, find the height from center of the wheel (setting the angle to its maximum of 20°):

$\implies \sin(20^{\circ})=\dfrac{h}{48}$

$\implies h=48\sin(20^{\circ})$

Then add it to the radius:

$\implies \sf max\:height=48\sin(20^{\circ})+45\tan(20^{\circ})=32.8\:in\:(1\:d.p.)$

(see diagram 4)

------------------------------------------------------------------------------------------

Circle Theorem vocabulary

Secant: a straight line that intersects a circle at two points.

Arc: the curve between two points on the circumference of a circle

Intercepted arc: the curve between the two points where two chords or line segments (that meet at one point on the other side of the circle) intercept the circumference of a circle.

Tangent: a straight line that touches a circle at only one point.

7 0

2 years ago

An unconfined compression test was performed to determine the average strength of concrete cylinders (in psi). It is believed th

Ronch [10]

Answer:

Explained below.

Step-by-step explanation:

(1)

The confidence level is, 91%.

Compute the value of α as follows:

$\text{Confidence level}\% =(100-\alpha \%)\\\\91% = 100-\alpha \%\\\\\alpha \%=100-91\%\\\\\alpha \%=9\%\\\\\alpha =0.09$

(2)

As the population standard deviation is provided, i.e. σ = 256 psi, the z value would be appropriate.

The z value for α = 0.09 is,

z = 1.69

(3)

Compute the 91% confidence interval as follows:

$CI=\bar x\pm z_{\alpha/2}\cdot\frac{\sigma}{\sqrt{n}}$

$=3000\pm 1.69\cdot\frac{256}{\sqrt{70}}\\\\=3000\pm 51.71\\\\=(2942.29, 3057.71)$

(4)

The 91% confidence interval for population mean implies that there is a 0.91 probability that the true value of the mean is included in the interval, (2942.29, 3057.71) psi.

8 0

2 years ago

Lupe’s Construction is building a rectangular house that is 16 feet longer than it is wide. They will be putting a 3-foot wide s

mr Goodwill [35]

Answer:

The length of the four pieces of protective strip is 96 feet

Step-by-step explanation:

Let the w be the width of the rectangular house and L is length. Since L = w + 16, its perimeter P = 2(w + L)

= 2(w + w + 16)

= 2(2w + 16)

Since the perimeter of the house P = 136 feet,

136 = 2(2w + 16)

dividing through by 2, we have

136/2 = (2w + 16)

68 = (2w + 16)

collecting like terms, we have

68 - 16 = 2w

52 = 2w

dividing through by 2, we have

w = 52/2

w = 26 feet.

Now, since the side walk is 3 foot wide all around, the width of the house plus sidewalk = w + 3 and the length of the house plus sidewalk = L + 3 = w + 16 + 3 = w + 19.

So, the perimeter of the house plus sidewalk which is the perimeter of the four pieces of protective strip is P' = 2(w + 3 + w + 19)

= 2(w + 22)

= 2(26 + 22)

= 2(48)

= 96 feet

So, the length of the four pieces of protective strip is 96 feet.

5 0

3 years ago

What is the wave speed of a wave that has a frequency of 25 Hz and a wavelength of 0.80 m?

tatuchka [14]

Answer:

Speed = 20 m/s

Step-by-step explanation:

The formula to find the speed of a wave is found by

Speed = Wavelength x Frequency where the frequency is in HZ and the wavelength is in meters

Speed = .80*25

Speed = 20 m/s

3 0

3 years ago

Read 2 more answers

Graph y=(x+2)^2-3 Show Vertex

nikklg [1K]

$\bf ~~~~~~\textit{parabola vertex form}
\\\\
\begin{array}{llll}
\boxed{y=a(x- h)^2+ k}\\\\
x=a(y- k)^2+ h
\end{array}
\qquad\qquad
vertex~~(\stackrel{}{ h},\stackrel{}{ k})\\\\
-------------------------------\\\\
y=(x+2)^2-3\implies y=\stackrel{a}{1}[x-\stackrel{h}{(-2)}]^2\stackrel{k}{-3}\quad 
\begin{cases}
h=-2\\
k=-3
\end{cases}$

3 0

3 years ago